reserve A,B,C for Category,
  F,F1 for Functor of A,B;
reserve o,m for set;
reserve t for natural_transformation of F,F1;

theorem Th18:
  for F being Functor of [:A,B:],C, a being Object of A holds (
  export F).a = F?-a
proof
  let F be Functor of [:A,B:],C, a be Object of A;
  reconsider o = F?-a as Object of Functors(B,C) by Th5;
  reconsider i = id a as Morphism of A;
  (export F).i = [[F?-a,F?-a],F?-id a] by Def4
    .= [[F?-a,F?-a],id(F?-a)] by Th16
    .= id o by NATTRA_1:def 17;
  hence thesis by CAT_1:67;
end;
